Multi-Solitons and Combined Solitons with Self-Similar Behaviors in a Birefringent Fiber with Higher-Order Effects

A coupled variable-coefficient higher-order nonlinear Schrödinger equation in birefringent fiber is studied, and analytical multi-soliton, combined bright and dark soliton, W-shaped and M-shaped soliton solutions are obtained. Nonlinear tunnelling of these combined solitons in dispersion barrier and dispersion well on an exponential background is discussed, and the decaying or increasing, even lossless tunnelling behaviors of combined solitons are decided by the decaying or increasing parameter.